Resource provisioning using predictive modeling in a networked computing environment

ABSTRACT

An approach is provided for allowing a network computing (e.g., cloud computing) infrastructure to modify its resource allocation plan (e.g., an instance count) by using a Kth derivative vector plot, which may be generated using historical logs. Among other things, this approach enables an infrastructure to project an allocation forecast for a specified duration and adapt to changes in network traffic.

CROSS-REFERENCE TO RELATED APPLICATIONS

The present patent document is a continuation of U.S. patent applicationSer. No. 13/593,920, filed Aug. 24, 2012, entitled “RESOURCEPROVISIONING USING PREDICTIVE MODELING IN A NETWORKED COMPUTINGENVIRONMENT”, the disclosure of which is incorporated herein byreference.

TECHNICAL FIELD

Embodiments of the present invention relate to computing resourceallocation in a networked computing environment (e.g., a cloud computingenvironment). Specifically, embodiments of the present invention relateto the utilization of historical web access logs and generation of aderivative vector plot (e.g., K^(th) derivative vector plot) that isused to provide forecasts of future events.

BACKGROUND

The networked computing environment (e.g., cloud computing environment)is an enhancement to the predecessor grid environment, whereby multiplegrids and other computation resources may be further enhanced by one ormore additional abstraction layers (e.g., a cloud layer), thus makingdisparate devices appear to an end-consumer as a single pool of seamlessresources. These resources may include such things as physical orlogical computing engines, servers and devices, device memory, andstorage devices, among others.

Cloud services may be rendered through dynamic infrastructureprovisioning. For example, within a relatively static hardware pool,operating systems and applications may be deployed and reconfigured tomeet dynamic customer computational demands. Within a cloudenvironment's boundaries, images may be installed and overwritten,Internet Protocol (IP) addresses may be modified, and real and virtualprocessors may be allocated to meet changing business needs. Challengesmay exist, however, in providing an infrastructure that is capable ofmodifying its resource allocation plan/protocol in response to changingdemands.

SUMMARY

Embodiments of the present invention provide an approach for allowing anetwork computing (e.g., cloud computing) infrastructure to modify itsresource allocation plan (e.g., an instance count) by using a K^(th)derivative vector plot, which may be generated using historical logs.Among other things, this approach enables an infrastructure to projectan allocation forecast for a specified duration and adapt to changes innetwork traffic.

A first aspect of the present invention provides a computer-implementedmethod for provisioning computing resources using predictive modeling ina networked computing environment, comprising: accessing a set ofgraphical curves of network data traffic versus time, the set ofgraphical curves being stored in at least one computer storage device;segmenting the set of graphical curves into a set of predetermined timeintervals to yield a set of time interval curves; overlaying and fittingthe set of time interval curves to yield a set of best fit overlayingcurves; generating a derivative vector plot based on a set of datapoints of the set of best fit overlaying curves; and forecasting networktraffic in the networked computing environment based on the derivativevector plot.

A second aspect of the present invention provides a system forprovisioning computing resources using predictive modeling in anetworked computing environment, comprising: a memory medium comprisinginstructions; a bus coupled to the memory medium; and a processorcoupled to the bus that when executing the instructions causes thesystem to: access a set of graphical curves of network data trafficversus time, the set of graphical curves being stored in at least onecomputer storage device; segment the set of graphical curves into a setof predetermined time intervals to yield a set of time interval curves;overlay and fit the set of time interval curves to yield a set of bestfit overlaying curves; generate a derivative vector plot based on a setof data points of the set of best fit overlaying curves; and forecastnetwork traffic in the networked computing environment based on thederivative vector plot.

A third aspect of the present invention provides a computer programproduct for provisioning computing resources using predictive modelingin a networked computing environment, the computer program productcomprising a computer readable storage media, and program instructionsstored on the computer readable storage media, to: access a set ofgraphical curves of network data traffic versus time, the set ofgraphical curves being stored in at least one computer storage device;segment the set of graphical curves into a set of predetermined timeintervals to yield a set of time interval curves; overlay and fit theset of time interval curves to yield a set of best fit overlayingcurves; generate a derivative vector plot based on a set of data pointsof the set of best fit overlaying curves; and forecast network trafficin the networked computing environment based on the derivative vectorplot.

A fourth aspect of the present invention provides a method for deployinga system for provisioning computing resources using predictive modelingin a networked computing environment, comprising: providing a computerinfrastructure being operable to: access a set of graphical curves ofnetwork data traffic versus time, the set of graphical curves beingstored in at least one computer storage device; segment the set ofgraphical curves into a set of predetermined time intervals to yield aset of time interval curves; overlay and fit the set of time intervalcurves to yield a set of best fit overlaying curves; generate aderivative vector plot based on a set of data points of the set of bestfit overlaying curves; and forecast network traffic in the networkedcomputing environment based on the derivative vector plot.

BRIEF DESCRIPTION OF THE DRAWINGS

These and other features of this invention will be more readilyunderstood from the following detailed description of the variousaspects of the invention taken in conjunction with the accompanyingdrawings in which:

FIG. 1 depicts a cloud computing node according to an embodiment of thepresent invention.

FIG. 2 depicts a cloud computing environment according to an embodimentof the present invention.

FIG. 3 depicts abstraction model layers according to an embodiment ofthe present invention.

FIG. 4 depicts a system diagram according to an embodiment of thepresent invention.

FIG. 5 depicts a set of overlaid plots/curves according to an embodimentof the present invention.

FIG. 6 depicts a derivative vector plot according to an embodiment ofthe present invention.

FIG. 7 depicts a method flow diagram according to an embodiment of thepresent invention

The drawings are not necessarily to scale. The drawings are merelyschematic representations, not intended to portray specific parametersof the invention. The drawings are intended to depict only typicalembodiments of the invention, and therefore should not be considered aslimiting the scope of the invention. In the drawings, like numberingrepresents like elements.

DETAILED DESCRIPTION

Illustrative embodiments will now be described more fully herein withreference to the accompanying drawings, in which embodiments are shown.This disclosure may, however, be embodied in many different forms andshould not be construed as limited to the embodiments set forth herein.Rather, these embodiments are provided so that this disclosure will bethorough and complete and will fully convey the scope of this disclosureto those skilled in the art. In the description, details of well-knownfeatures and techniques may be omitted to avoid unnecessarily obscuringthe presented embodiments.

The terminology used herein is for the purpose of describing particularembodiments only and is not intended to be limiting of this disclosure.As used herein, the singular forms “a”, “an”, and “the” are intended toinclude the plural forms as well, unless the context clearly indicatesotherwise. Furthermore, the use of the terms “a”, “an”, etc., do notdenote a limitation of quantity, but rather denote the presence of atleast one of the referenced items. The term “set” is intended to mean aquantity of at least one. It will be further understood that the terms“comprises” and/or “comprising”, or “includes” and/or “including”, whenused in this specification, specify the presence of stated features,regions, integers, steps, operations, elements, and/or components, butdo not preclude the presence or addition of one or more other features,regions, integers, steps, operations, elements, components, and/orgroups thereof.

Embodiments of the present invention provide an approach for allowing anetwork computing (e.g., cloud computing) infrastructure to modify itsresource allocation plan (e.g., an instance count) by using a K^(th)derivative vector plot, which may be generated using historical logs.Among other things, this approach enables an infrastructure to projectan allocation forecast for a specified duration and adapt to changes innetwork traffic.

It is understood in advance that although this disclosure includes adetailed description of cloud computing, implementation of the teachingsrecited herein are not limited to a cloud computing environment. Rather,embodiments of the present invention are capable of being implemented inconjunction with any other type of computing environment now known orlater developed.

Cloud computing is a model of service delivery for enabling convenient,on-demand network access to a shared pool of configurable computingresources (e.g. networks, network bandwidth, servers, processing,memory, storage, applications, virtual machines, and services) that canbe rapidly provisioned and released with minimal management effort orinteraction with a provider of the service. This cloud model may includeat least five characteristics, at least three service models, and atleast four deployment models.

Characteristics are as follows:

On-demand self-service: a cloud consumer can unilaterally provisioncomputing capabilities, such as server time and network storage, asneeded, automatically without requiring human interaction with theservice's provider.

Broad network access: capabilities are available over a network andaccessed through standard mechanisms that promote use by heterogeneousthin or thick client platforms (e.g., mobile phones, laptops, and PDAs).

Resource pooling: the provider's computing resources are pooled to servemultiple consumers using a multi-tenant model, with different physicaland virtual resources dynamically assigned and reassigned according todemand. There is a sense of location independence in that the consumergenerally has no control or knowledge over the exact location of theprovided resources but may be able to specify location at a higher levelof abstraction (e.g., country, state, or datacenter).

Rapid elasticity: capabilities can be rapidly and elasticallyprovisioned, in some cases automatically, to quickly scale out andrapidly released to quickly scale in. To the consumer, the capabilitiesavailable for provisioning often appear to be unlimited and can bepurchased in any quantity at any time.

Measured service: cloud systems automatically control and optimizeresource use by leveraging a metering capability at some level ofabstraction appropriate to the type of service (e.g., storage,processing, bandwidth, and active consumer accounts). Resource usage canbe monitored, controlled, and reported providing transparency for boththe provider and consumer of the utilized service.

Service Models are as follows:

Software as a Service (SaaS): the capability provided to the consumer isto use the provider's applications running on a cloud infrastructure.The applications are accessible from various client devices through athin client interface such as a web browser (e.g., web-based email). Theconsumer does not manage or control the underlying cloud infrastructureincluding network, servers, operating systems, storage, or evenindividual application capabilities, with the possible exception oflimited consumer-specific application configuration settings.

Platform as a Service (PaaS): the capability provided to the consumer isto deploy onto the cloud infrastructure consumer-created or acquiredapplications created using programming languages and tools supported bythe provider. The consumer does not manage or control the underlyingcloud infrastructure including networks, servers, operating systems, orstorage, but has control over the deployed applications and possiblyapplication-hosting environment configurations.

Infrastructure as a Service (IaaS): the capability provided to theconsumer is to provision processing, storage, networks, and otherfundamental computing resources where the consumer is able to deploy andrun arbitrary software, which can include operating systems andapplications. The consumer does not manage or control the underlyingcloud infrastructure but has control over operating systems, storage,deployed applications, and possibly limited control of select networkingcomponents (e.g., host firewalls).

Deployment Models are as follows:

Private cloud: the cloud infrastructure is operated solely for anorganization. It may be managed by the organization or a third party andmay exist on-premises or off-premises.

Community cloud: the cloud infrastructure is shared by severalorganizations and supports a specific community that has shared concerns(e.g., mission, security requirements, policy, and complianceconsiderations). It may be managed by the organizations or a third partyand may exist on-premises or off-premises.

Public cloud: the cloud infrastructure is made available to the generalpublic or a large industry group and is owned by an organization sellingcloud services.

Hybrid cloud: the cloud infrastructure is a composition of two or moreclouds (private, community, or public) that remain unique entities butare bound together by standardized or proprietary technology thatenables data and application portability (e.g., cloud bursting forload-balancing between clouds).

A cloud computing environment is service oriented with a focus onstatelessness, low coupling, modularity, and semantic interoperability.At the heart of cloud computing is an infrastructure comprising anetwork of interconnected nodes.

Referring now to FIG. 1, a schematic of an example of a cloud computingnode is shown. Cloud computing node 10 is only one example of a suitablecloud computing node and is not intended to suggest any limitation as tothe scope of use or functionality of embodiments of the inventiondescribed herein. Regardless, cloud computing node 10 is capable ofbeing implemented and/or performing any of the functionality set forthhereinabove.

In cloud computing node 10, there is a computer system/server 12, whichis operational with numerous other general purpose or special purposecomputing system environments or configurations. Examples of well-knowncomputing systems, environments, and/or configurations that may besuitable for use with computer system/server 12 include, but are notlimited to, personal computer systems, server computer systems, thinclients, thick clients, hand-held or laptop devices, multiprocessorsystems, microprocessor-based systems, set top boxes, programmableconsumer electronics, network PCs, minicomputer systems, mainframecomputer systems, and distributed cloud computing environments thatinclude any of the above systems or devices, and the like.

Computer system/server 12 may be described in the general context ofcomputer system-executable instructions, such as program modules, beingexecuted by a computer system. Generally, program modules may includeroutines, programs, objects, components, logic, data structures, and soon that perform particular tasks or implement particular abstract datatypes. Computer system/server 12 may be practiced in distributed cloudcomputing environments where tasks are performed by remote processingdevices that are linked through a communications network. In adistributed cloud computing environment, program modules may be locatedin both local and remote computer system storage media including memorystorage devices.

As shown in FIG. 1, computer system/server 12 in cloud computing node 10is shown in the form of a general-purpose computing device. Thecomponents of computer system/server 12 may include, but are not limitedto, one or more processors or processing units 16, a system memory 28,and a bus 18 that couples various system components including systemmemory 28 to processor 16.

Bus 18 represents one or more of any of several types of bus structures,including a memory bus or memory controller, a peripheral bus, anaccelerated graphics port, and a processor or local bus using any of avariety of bus architectures. By way of example, and not limitation,such architectures include Industry Standard Architecture (ISA) bus,Micro Channel Architecture (MCA) bus, Enhanced ISA (EISA) bus, VideoElectronics Standards Association (VESA) local bus, and PeripheralComponent Interconnects (PCI) bus.

Computer system/server 12 typically includes a variety of computersystem readable media. Such media may be any available media that isaccessible by computer system/server 12, and it includes both volatileand non-volatile media, removable and non-removable media.

System memory 28 can include computer system readable media in the formof volatile memory, such as random access memory (RAM) 30 and/or cachememory 32. Computer system/server 12 may further include otherremovable/non-removable, volatile/non-volatile computer system storagemedia. By way of example only, storage system 34 can be provided forreading from and writing to a non-removable, non-volatile magnetic media(not shown and typically called a “hard drive”). Although not shown, amagnetic disk drive for reading from and writing to a removable,non-volatile magnetic disk (e.g., a “floppy disk”), and an optical diskdrive for reading from or writing to a removable, non-volatile opticaldisk such as a CD-ROM, DVD-ROM, or other optical media can be provided.In such instances, each can be connected to bus 18 by one or more datamedia interfaces. As will be further depicted and described below,memory 28 may include at least one program product having a set (e.g.,at least one) of program modules that are configured to carry out thefunctions of embodiments of the invention.

The embodiments of the invention may be implemented as a computerreadable signal medium, which may include a propagated data signal withcomputer readable program code embodied therein (e.g., in baseband or aspart of a carrier wave). Such a propagated signal may take any of avariety of forms including, but not limited to, electro-magnetic,optical, or any suitable combination thereof. A computer readable signalmedium may be any computer readable medium that is not a computerreadable storage medium and that can communicate, propagate, ortransport a program for use by or in connection with an instructionexecution system, apparatus, or device.

Program code embodied on a computer readable medium may be transmittedusing any appropriate medium including, but not limited to, wireless,wireline, optical fiber cable, radio-frequency (RF), etc., or anysuitable combination of the foregoing.

Program/utility 40, having a set (at least one) of program modules 42,may be stored in memory 28 by way of example, and not limitation, aswell as an operating system, one or more application programs, otherprogram modules, and program data. Each of the operating system, one ormore application programs, other program modules, and program data orsome combination thereof, may include an implementation of a networkingenvironment. Program modules 42 generally carry out the functions and/ormethodologies of embodiments of the invention as described herein.

Computer system/server 12 may also communicate with one or more externaldevices 14 such as a keyboard, a pointing device, a display 24, etc.;one or more devices that enable a consumer to interact with computersystem/server 12; and/or any devices (e.g., network card, modem, etc.)that enable computer system/server 12 to communicate with one or moreother computing devices. Such communication can occur via I/O interfaces22. Still yet, computer system/server 12 can communicate with one ormore networks such as a local area network (LAN), a general wide areanetwork (WAN), and/or a public network (e.g., the Internet) via networkadapter 20. As depicted, network adapter 20 communicates with the othercomponents of computer system/server 12 via bus 18. It should beunderstood that although not shown, other hardware and/or softwarecomponents could be used in conjunction with computer system/server 12.Examples include, but are not limited to: microcode, device drivers,redundant processing units, external disk drive arrays, RAID systems,tape drives, and data archival storage systems, etc.

Referring now to FIG. 2, illustrative cloud computing environment 50 isdepicted. As shown, cloud computing environment 50 comprises one or morecloud computing nodes 10 with which local computing devices used bycloud consumers, such as, for example, personal digital assistant (PDA)or cellular telephone 54A, desktop computer 54B, laptop computer 54C,and/or automobile computer system 54N may communicate. Nodes 10 maycommunicate with one another. They may be grouped (not shown) physicallyor virtually, in one or more networks, such as private, community,public, or hybrid clouds as described hereinabove, or a combinationthereof. This allows cloud computing environment 50 to offerinfrastructure, platforms, and/or software as services for which a cloudconsumer does not need to maintain resources on a local computingdevice. It is understood that the types of computing devices 54A-N shownin FIG. 2 are intended to be illustrative only and that computing nodes10 and cloud computing environment 50 can communicate with any type ofcomputerized device over any type of network and/or network addressableconnection (e.g., using a web browser).

Referring now to FIG. 3, a set of functional abstraction layers providedby cloud computing environment 50 (FIG. 2) is shown. It should beunderstood in advance that the components, layers, and functions shownin FIG. 3 are intended to be illustrative only and embodiments of theinvention are not limited thereto. As depicted, the following layers andcorresponding functions are provided:

Hardware and software layer 60 includes hardware and softwarecomponents. Examples of hardware components include mainframes. In oneexample, IBM® zSeries® systems and RISC (Reduced Instruction SetComputer) architecture based servers. In one example, IBM pSeries®systems, IBM System X® servers, IBM BladeCenter® systems, storagedevices, networks, and networking components. Examples of softwarecomponents include network application server software. In one example,IBM WebSphere® application server software and database software. In oneexample, IBM DB2® database software. (IBM, zSeries, pSeries, System x,BladeCenter, WebSphere, and DB2 are trademarks of International BusinessMachines Corporation registered in many jurisdictions worldwide.)

Virtualization layer 62 provides an abstraction layer from which thefollowing examples of virtual entities may be provided: virtual servers;virtual storage; virtual networks, including virtual private networks;virtual applications and operating systems; and virtual clients.

In one example, management layer 64 may provide the functions describedbelow. Resource provisioning provides dynamic procurement of computingresources and other resources that are utilized to perform tasks withinthe cloud computing environment. Metering and pricing provide costtracking as resources are utilized within the cloud computingenvironment, and billing or invoicing for consumption of theseresources. In one example, these resources may comprise applicationsoftware licenses. Security provides identity verification for cloudconsumers and tasks, as well as protection for data and other resources.Consumer portal provides access to the cloud computing environment forconsumers and system administrators. Service level management providescloud computing resource allocation and management such that requiredservice levels are met. Service Level Agreement (SLA) planning andfulfillment provides pre-arrangement for, and procurement of, cloudcomputing resources for which a future requirement is anticipated inaccordance with an SLA. Further shown in management layer is predictivemodeling(-based) resource allocation, which represents the functionalitythat is provided under the embodiments of the present invention.

Workloads layer 66 provides examples of functionality for which thecloud computing environment may be utilized. Examples of workloads andfunctions which may be provided from this layer include: mapping andnavigation; software development and lifecycle management; virtualclassroom education delivery; data analytics processing; transactionprocessing; and consumer data storage and backup. As mentioned above,all of the foregoing examples described with respect to FIG. 3 areillustrative only, and the invention is not limited to these examples.

It is understood that all functions of the present invention asdescribed herein typically may be performed by the predictive modelingresource allocation functionality (of management layer 64, which can betangibly embodied as modules of program code 42 of program/utility 40(FIG. 1). However, this need not be the case. Rather, the functionalityrecited herein could be carried out/implemented and/or enabled by any ofthe layers 60-66 shown in FIG. 3.

It is reiterated that although this disclosure includes a detaileddescription on cloud computing, implementation of the teachings recitedherein are not limited to a cloud computing environment. Rather, theembodiments of the present invention are intended to be implemented withany type of networked computing environment now known or laterdeveloped.

Referring now to FIG. 4, a system diagram describing the functionalitydiscussed herein according to an embodiment of the present invention isshown. It is understood that the teachings recited herein may bepracticed within any type of networked computing environment 86 (e.g., acloud computing environment 50). A computer system/server 12, which canbe implemented as either a stand-alone computer system or as a networkedcomputer system is shown in FIG. 4. In the event the teachings recitedherein are practiced in a networked computing environment 86, eachclient need not have a predictive modeling resource allocation engine(engine 70). Rather, engine 70 could be loaded on a server orserver-capable device that communicates (e.g., wirelessly) with theclients to provide predictive modeling-based resource allocationtherefor. Regardless, as depicted, engine 70 is shown within computersystem/server 12. In general, engine 70 can be implemented asprogram/utility 40 on computer system 12 of FIG. 1 and can enable thefunctions recited herein. As further shown, engine 70 (in oneembodiment) comprises a rules and/or computational engine that processesa set (at least one) of rules/logic 72 and/or provides predictivemodeling-based computing resource allocation hereunder.

Along these lines, engine 70 may perform multiple functions similar to ageneral-purpose computer. Specifically, among other functions, engine 70may (among other things): receive a set of data feeds 74A-N; determinenetwork traffic based on the set of data feeds 74A-N (e.g., socialnetworking feeds); generate a set of graphical curves 80A-N based on thenetwork traffic (e.g., for storage in one or more computer storagedevices 78); access a set of graphical curves 80A-N of network datatraffic versus time; segment the set of graphical curves 80A-N into aset of predetermined time intervals to yield a set of time intervalcurves 82A-N; overlay and fit the set of time interval curves 82A-N toyield a set of best fit overlaying curves; generate a derivative vectorplot 84 (e.g., a K^(th) derivative vector plot) based on a set of datapoints of the set of best fit overlaying curves; integrate K initialconditions of a K quantity of times using a predetermined numericaltechnique (e.g., a fourth order Runge-Kutta technique); forecast networktraffic in the networked computing environment 86 based on derivativevector plot 84; provision a set of computing resources 88A-N in thenetworked computing environment based on the forecasted network traffic;and/or output a network traffic projection 90 based on the forecasting.

As can be seen, embodiments of the present invention utilize concepts ofpredictive modeling and forecasting, vector fields, and/or derivatives.These concepts will be further described below:

Predictive Models and Forecasting

Predictive models analyze past performance to assess the likelihood of aspecific event to occur in the future. Similarly, forecasting is theprocess of making statements about events whose actual outcomestypically have not yet been observed. This category also encompassesmodels that seek out subtle data patterns for future forecasting.Predictive models often perform calculations during live transactions,and with the advancement in computing speed, modeling systems caneffectively be used for forecasting or predictions.

Vector Fields and Derivatives

In calculus, a vector field, or plot, is an assignment of a vector toeach point in a subset of Euclidean space. A vector plot in the plane,for instance, may be visualized as a collection of arrows with a givenmagnitude and direction attached to each point in the plane. Incalculus, a derivative is a measurement of how a function changes as itsinputs change. A derivative may be thought of as how much one quantityis changing in response to changes in some other quantity. For example,the derivative of a position of a moving object with respect to time isthe object's instantaneous velocity. The elements of differential andintegral calculus extend to vector fields in a natural way. Vectorfields may be thought of as representing the velocity of a moving flowin space.

Illustrative Example

The embodiments of the present invention may be understood with thefollowing example. It is understood, however, that this example isintended to be illustrative only and not limiting the teachings recitedherein. Assume in this example that an events private cloud is providedthat is tasked with developing the infrastructure to deliver brandcritical web sites such as IBM.com (IBM and related terms are trademarksof International Business Machines Corporation in the United Statesand/or other countries) to a major sporting event. The embodimentsdiscussed herein may utilize historical web access logs from theduration of such respective events, and generate a K^(th) derivativevector plot that is used to provide forecasts of future similar events.The embodiments of the present invention may enable cloud environmentsto predict required resource allocations, allocate those resources asrequired, and modify those resources continuously and accurately.

Along these lines, embodiments of the present invention may utilizemathematical measures, such as differential and integral calculus, anderror minimization to generate a K^(th) derivative vector plot. The plotmay then be utilized to generate a resource utilization/allocationprojection/plan. This may be accomplished as follows:

-   -   1. Using each individual day's traffic, create an aggregate best        fitting overlay. This may be achieved by minimizing the error in        fitting the curves for each day's traffic by using the following        steps:        -   A. Splice/segment the historical traffic into individual            periods. For example, in the events private cloud, the            historical traffic may be spliced on local minimums.        -   B. Overlay the resulting curves and minimize the error in            fitting the curves. For example, in the events private            cloud, an error function may be defined as the integral of            the square of the ordinate distance between interpolated            traffic curves. This may be minimized by varying curve            characteristics. More specifically, the events private cloud            may use Powell Optimization to minimize the error by            altering the amplitudes of the traffic curves, shifting the            abscissae, and shifting the ordinates.        -   C. Maintain the characteristics that are pertinent by            reverting their alterations. For example, in the events            private cloud, only the abscissa shift is reflected in the            final overlay. The ordinate shift and amplitude changes are            reverted.    -   2. Generate a K^(th) derivative vector for each point on each        best-fit overlaying curve. Then, superimpose the vectors onto a        unified vector plot at their respective initial abscissa and        ordinate. For example, in the events private cloud, a second        derivative vector plot is generated from all relevant historical        event data.        Forecasting

Based on the generated K^(th) derivative vector plot, the embodimentsmay then process real time web access log data. The vector plot may takethe volume and trend (direction) of the current log data as inputs tooutput an instantaneous traffic projection for the next period. This maybe achieved by taking K initial conditions and integrating K times usinga numerical integration technique. For example, in the events privatecloud, the current position (abscissa, ordinate) and velocity (slope)are used as initial conditions and a fourth order Runge-Kutta method isapplied to the vector plot with sufficiently small time change (Δt) andcarried out over a predetermined period (e.g., 24 hours).

Fourth Order Runge-Kutta Method

As indicated above, a 4^(th) order Runge-Kutta method (RK4) may beutilized hereunder. Shown below is a brief description of this method.

Let an initial value problem be specified as follows.

=f(t,

),

(t ₀)=

₀.

This expression generally means that the rate at which y changes is afunction of y itself and of t (time). At the start, time is t₀ and y is

₀. In the equation, y may be a scalar or a vector. The RK4 method forthis problem may be given by the following equations:

$y_{n + 1} = {y_{n} + {\frac{1}{6}\left( {k_{1} + {2k_{2}} + {2k_{3}} + k_{4}} \right)}}$t_(n + 1) − t_(n) + hwhere

_(n+1) is the RK4 approximation of

(t_(n+1)), and

${k_{1} = {h\;{f\left( {t_{n},y_{n}} \right)}}},{k_{2} = {h\;{f\left( {{t_{n} + {\frac{1}{2}h}},{y_{n} + {\frac{1}{2}k_{1}}}} \right)}}},{k_{3} = {h\;{f\left( {{t_{n} + {\frac{1}{2}h}},{y_{n} + {\frac{1}{2}k_{2}}}} \right)}}},{k_{4} = {h\;{{f\left( {{t_{n} + h},{y_{n} + k_{3}}} \right)}.}}}$Thus, the next value (

_(n+1)) is determined by the present value (

_(n)) plus the weighted average of four increments, where each incrementis the product of the size of the interval h, and an estimated slopespecified by function f on the right-hand side of the differentialequation. The variables indicated above may be defined as follows:

-   -   k₁ is the increment based on the slope at the beginning of the        interval, using        _(n) (e.g., Euler's method);    -   k₂ is the increment based on the slope at the midpoint of the        interval, using

${y_{n} + {\frac{1}{2}k_{1}}};$

-   -   k₃ is again the increment based on the slope at the midpoint,        but now using

${y_{n} + {\frac{1}{2}k_{2}}};$

-   -    and    -   k₄ is the increment based on the slope at the end of the        interval, using        _(n)+k₃.

In averaging the four increments, greater weight is given to theincrements at the midpoint. The weights are chosen such that if f isindependent of

, so that the differential equation is equivalent to a simple integral,then RK4 is Simpson's rule. The RK4 method is a fourth-order method,meaning that the error per step is on the order of h⁵, while the totalaccumulated error has order h⁴.

Derivation of Fourth Order Runge-Kutta Method

In general a Runge-Kutta method of order s can be written as:

$y_{t + h} = {y_{t} + {h \cdot {\sum\limits_{i = 1}^{s}\;{a_{i}k_{i}}}} + {{??}\left( h^{s + 1} \right)}}$where:$k_{i} = {f\left( {{y_{t} + {h \cdot {\sum\limits_{j = 1}^{s}\;{\beta_{i\; j}k_{j}}}}},{t_{n} - {\alpha_{i}h}}} \right)}$are increments obtained evaluating the derivatives of

_(t) at the i-th order. We develop the derivation for the Runge-Kuttafourth order method using the general formula with s=4 evaluated, asexplained above, at the starting point, the midpoint and the end pointof any interval (t,t+h), thus we choose:

$\begin{matrix}\alpha_{i} & \beta_{i} \\{\alpha_{1} = 0} & {\beta_{21} = \frac{1}{2}} \\{\alpha_{2} = \frac{1}{2}} & {\beta_{32} = \frac{1}{2}} \\{\alpha_{3} = \frac{1}{2}} & {\beta_{43} = 1} \\{\alpha_{4} = 1} & \;\end{matrix}$and β_(ij)=0 otherwise. We begin by defining the following quantities:

y_(t + h)¹ = y_(t) + h f(y_(t), t)$y_{t + h}^{2} = {y_{t} + {h\;{f\left( {y_{t + {h/2}}^{1},{t + \frac{h}{2}}} \right)}}}$$y_{t + h}^{3} - y_{t} + {h\;{f\left( {y_{t + {h/2}}^{2},{t + \frac{h}{2}}} \right)}}$where

$y_{t + {h/2}}^{1} - {\frac{y_{t} + y_{t + h}^{1}}{1}\mspace{14mu}{and}\mspace{14mu} y_{t + {h/2}}^{2}} - \frac{y_{t} + y_{t + h}^{2}}{1}$If we define:

k₁ = f(y_(t), t)$k_{2} = {f\left( {y_{t + {h/2}}^{1},{t + \frac{h}{2}}} \right)}$$k_{3} = {f\left( {y_{t + {h/2}}^{2},{t + \frac{h}{2}}} \right)}$k₄ = f(y_(t + h)³, t + h)and for the previous relations we can show that the following equalitiesholds up to

(h²):

$\begin{matrix}{k_{2} = {{f\left( {y_{t + {h/2}}^{1},{t + \frac{h}{2}}} \right)} = {f\left( {{y_{t} + {\frac{h}{2}k_{1}}},{t + \frac{h}{2}}} \right)}}} \\{= {{f\left( {y_{t},t} \right)} - {\frac{h}{2}\frac{d}{d\; t}{f\left( {y_{t},t} \right)}}}}\end{matrix}$ $\begin{matrix}{k_{3} = {{f\left( {y_{t + {h/2}}^{2},{t + \frac{h}{2}}} \right)} = {f\left( {{y_{t} + {\frac{h}{2}{f\left( {{y_{t} + {\frac{h}{2}k_{1}}},{t + \frac{h}{2}}} \right)}}},{t + \frac{h}{2}}} \right)}}} \\{= {{f\left( {y_{t},t} \right)} - {\frac{h}{2}{\frac{d}{d\; t}\left\lbrack {{f\left( {y_{t},t} \right)} + {\frac{h}{2}\frac{d}{d\; t}{f\left( {y_{t},t} \right)}}} \right\rbrack}}}}\end{matrix}$ $\begin{matrix}{k_{4} = {{f\left( {y_{t + h}^{3},{t + h}} \right)} = {f\left( {{y_{t} + {h\;{f\left( {{y_{t} + {\frac{h}{2}k_{2}}},{t + \frac{h}{2}}} \right)}}},{t + h}} \right)}}} \\{= {f\left( {{y_{t} + {h\;{f\left( {{y_{t} + {\frac{h}{2}{f\left( {{y_{t} + {\frac{h}{2}{f\left( {y_{t},t} \right)}}},{t + \frac{h}{2}}} \right)}}},{t + \frac{h}{2}}} \right)}}},{t + h}} \right)}} \\{= {{f\left( {y_{t},t} \right)} - {h{\frac{d}{d\; t}\left\lbrack {{f\left( {y_{t},t} \right)} + {\frac{h}{2}{\frac{d}{d\; t}\left\lbrack {{f\left( {y_{t},t} \right)} + {\frac{h}{2}\frac{d}{d\; t}{f\left( {y_{t},t} \right)}}} \right\rbrack}}} \right\rbrack}}}}\end{matrix}$where:

${\frac{d}{d\; t}{f\left( {y_{t},t} \right)}} = {{{\frac{\partial}{\partial y}{f\left( {y_{t},y} \right)}{\overset{.}{y}}_{t}} + {\frac{\partial}{\partial t}{f\left( {y_{t},t} \right)}}} = {{{{f_{y}\left( {y_{t},t} \right)}\overset{.}{y}} + {f_{t}\left( {y_{t},t} \right)}}:={\overset{¨}{y}}_{t}}}$is the total derivative of f with respect to time. If we now express thegeneral formula using what we just derived, we obtain:

$\begin{matrix}{y_{t + h} = {y_{t} + {h\left\{ {{a \cdot {f\left( {y_{t},t} \right)}} + {b \cdot {\left\lbrack {{f\left( {y_{t},t} \right)} + {\frac{h}{2}\frac{d}{d\; t}{f\left( {y_{t},t} \right)}}} \right\rbrack++}}} \right.}}} \\{c \cdot {\left\lbrack {{f\left( {y_{t},t} \right)} + {\frac{h}{2}{\frac{d}{d\; t}\left\lbrack {{f\left( {y_{t},t} \right)} + {\frac{h}{2}\frac{d}{d\; t}{f\left( {y_{t},t} \right)}}} \right\rbrack}}} \right\rbrack++}} \\{d \cdot \left\lbrack {{f\left( {y_{t},t} \right)} + {h{\frac{d}{d\; t}\left\lbrack {{f\left( {y_{t},t} \right)} + {\frac{h}{2}{\frac{d}{d\; t}\left\lbrack {{f\left( {y_{t},t} \right)} +} \right.}}} \right.}}} \right.} \\{\left. \left. \left. \left. {\frac{h}{2}\frac{d}{d\; t}{f\left( {y_{t},t} \right)}} \right\rbrack \right\rbrack \right\rbrack \right\} + {{??}\left( h^{5} \right)}} \\{= {y_{t} + {{a \cdot h}\; f_{t}} + {{b \cdot h}\; f_{t}} + {{b \cdot \frac{h^{2}}{2}}\frac{d\; f_{t}}{d\; t}} + {{c \cdot h}\; f_{t}} + {{c \cdot \frac{h^{2}}{2}}{\frac{d\; f_{t}}{d\; t}++}}}} \\{{{c \cdot \frac{h^{3}}{4}}\frac{d^{2}f_{t}}{d\; t^{2}}} + {{d \cdot h}\; f_{t}} + {{d \cdot h^{2}}\frac{d\; f_{t}}{d\; t}} + {{d \cdot \frac{h^{3}}{2}}\frac{d^{2}f_{t}}{d\; t^{2}}} +} \\{{{d \cdot \frac{h^{4}}{4}}\frac{d^{3}f_{t}}{d\; t^{3}}} + {{??}\left( h^{5} \right)}}\end{matrix}$and comparing this with the Taylor series of

_(t+h) around

_(t):

${y_{t + h} - y_{t} + {h{\overset{.}{y}}_{t}} + {\frac{h^{2}}{2}{\overset{¨}{y}}_{t}} + {\frac{h^{3}}{6}y_{t}^{(3)}} + {\frac{h^{4}}{24}y_{t}^{(4)}} + {{??}\left( h^{5} \right)}}-={y_{t} + {h\;{f\left( {y_{t},t} \right)}} + {\frac{h^{2}}{2}\frac{d}{d\; t}{f\left( {y_{t},t} \right)}} - {\frac{h^{3}}{6}\frac{d^{2}}{d\; t^{2}}{f\left( {y_{t},t} \right)}} + {\frac{h^{4}}{24}\frac{d^{3}}{d\; t^{3}}{f\left( {y_{t},t} \right)}}}$we obtain a system of constraints on the coefficients:

$\quad\left\{ \begin{matrix}{{a + b + c + d} = 1} \\{{{\frac{1}{2}b} + {\frac{1}{2}c} + d} = \frac{1}{2}} \\{{{\frac{1}{4}c} + {\frac{1}{2}d}} = \frac{1}{6}} \\{{\frac{1}{4}d} = \frac{1}{24}}\end{matrix} \right.$which solved gives

${a = \frac{1}{6}},{b = \frac{1}{3}},{c = \frac{1}{3}},{d = \frac{1}{6}}$as stated above. It is understood that these computations/algorithms aretypically performed/calculated by engine 70.

Referring now to FIG. 5, a graph 100 of network traffic rate of requestsper minute (y-axis) versus time (x-axis) is shown. In general, graph 100depicts data points 102 for overlaid time segments (e.g., plots/curves104A-C). Segments 104A-C may pertain to a common time period occurringin consecutive days, weeks, months, etc. By overlaying and fittingplots/curves 104A-C, data outliers may be reduced and a more accuratedepiction of network traffic versus time may be obtained. Specifically,graph 100 represents a second derivative vector that is created atmultiple points over each of a set of daily traffic plots 104A-C (e.g.,corresponding to 82A-N of FIG. 4). Each of the plots 104A-C may besuperimposed to form a vector field.

Referring now to FIG. 6, a graph 200 having a single predictivecurve/plot 202 is shown. In general, vector plot 200 is generated (e.g.,by engine 70 of FIG. 4) by utilizing a fourth-order Runge-Kutta methodto integrate over the second-derivative vector plot 100 of FIG. 5 (e.g.,with initial conditions specified by the current traffic) to generate aforecast for the remainder of a period to be generated. Curve 202 allowspotential future network traffic to be forested (e.g., extrapolated).

Referring now to FIG. 7, a method flow diagram according to anembodiment of the present invention is depicted. In step S1, a set ofgraphical curves of network data traffic versus time is accessed. Theset of graphical curves may be stored in at least one computer storagedevices. In step S2, the set of graphical curves is segmented into a setof predetermined time intervals to yield a set of time interval curves.In step S3, the set of time interval curves will be overlaid and fittedto yield a set of best fit overlaying curves. In step S4, a derivativevector plot will be generated based on a set of data points of the setof best fit overlaying curves. In step S5, network traffic in thenetworked computing environment will be forecasted based on thederivative vector plot.

While shown and described herein as a predictive modeling-based resourceallocation solution, it is understood that the invention furtherprovides various alternative embodiments. For example, in oneembodiment, the invention provides a computer-readable/useable mediumthat includes computer program code to enable a computer infrastructureto provide predictive modeling-based resource allocation functionalityas discussed herein. To this extent, the computer-readable/useablemedium includes program code that implements each of the variousprocesses of the invention. It is understood that the termscomputer-readable medium or computer-useable medium comprise one or moreof any type of physical embodiment of the program code. In particular,the computer-readable/useable medium can comprise program code embodiedon one or more portable storage articles of manufacture (e.g., a compactdisc, a magnetic disk, a tape, etc.), on one or more data storageportions of a computing device, such as memory 28 (FIG. 1) and/orstorage system 34 (FIG. 1) (e.g., a fixed disk, a read-only memory, arandom access memory, a cache memory, etc.).

In another embodiment, the invention provides a method that performs theprocess of the invention on a subscription, advertising, and/or feebasis. That is, a service provider, such as a Solution Integrator, couldoffer to provide predictive modeling-based resource allocationfunctionality. In this case, the service provider can create, maintain,support, etc., a computer infrastructure, such as computer system 12(FIG. 1) that performs the processes of the invention for one or moreconsumers. In return, the service provider can receive payment from theconsumer(s) under a subscription and/or fee agreement and/or the serviceprovider can receive payment from the sale of advertising content to oneor more third parties.

In still another embodiment, the invention provides acomputer-implemented method for predictive modeling-based resourceallocation. In this case, a computer infrastructure, such as computersystem 12 (FIG. 1), can be provided and one or more systems forperforming the processes of the invention can be obtained (e.g.,created, purchased, used, modified, etc.) and deployed to the computerinfrastructure. To this extent, the deployment of a system can compriseone or more of: (1) installing program code on a computing device, suchas computer system 12 (FIG. 1), from a computer-readable medium; (2)adding one or more computing devices to the computer infrastructure; and(3) incorporating and/or modifying one or more existing systems of thecomputer infrastructure to enable the computer infrastructure to performthe processes of the invention.

As used herein, it is understood that the terms “program code” and“computer program code” are synonymous and mean any expression, in anylanguage, code, or notation, of a set of instructions intended to causea computing device having an information processing capability toperform a particular function either directly or after either or both ofthe following: (a) conversion to another language, code, or notation;and/or (b) reproduction in a different material form. To this extent,program code can be embodied as one or more of: an application/softwareprogram, component software/a library of functions, an operating system,a basic device system/driver for a particular computing device, and thelike.

A data processing system suitable for storing and/or executing programcode can be provided hereunder and can include at least one processorcommunicatively coupled, directly or indirectly, to memory elementsthrough a system bus. The memory elements can include, but are notlimited to, local memory employed during actual execution of the programcode, bulk storage, and cache memories that provide temporary storage ofat least some program code in order to reduce the number of times codemust be retrieved from bulk storage during execution. Input/outputand/or other external devices (including, but not limited to, keyboards,displays, pointing devices, etc.) can be coupled to the system eitherdirectly or through intervening device controllers.

Network adapters also may be coupled to the system to enable the dataprocessing system to become coupled to other data processing systems,remote printers, storage devices, and/or the like, through anycombination of intervening private or public networks. Illustrativenetwork adapters include, but are not limited to, modems, cable modems,and Ethernet cards.

The foregoing description of various aspects of the invention has beenpresented for purposes of illustration and description. It is notintended to be exhaustive or to limit the invention to the precise formdisclosed and, obviously, many modifications and variations arepossible. Such modifications and variations that may be apparent to aperson skilled in the art are intended to be included within the scopeof the invention as defined by the accompanying claims.

What is claimed is:
 1. A computer-implemented method for provisioningcomputing resources using predictive modeling in a networked computingenvironment, comprising: segmenting a set of graphical curves of networkdata traffic versus time generated from historical logs of networktraffic into a set of predetermined time intervals to yield a set oftime interval curves; overlaying and fitting the set of time intervalcurves to yield a set of best fit overlaying curves; generating aderivative vector plot based on a set of data points of the set of bestfit overlaying curves; forecasting network traffic in the networkedcomputing environment based on the derivative vector plot; and modifyingan allocation of a set of computing resources in the networked computingenvironment based on the forecasted network traffic.
 2. Thecomputer-implemented method of claim 1, further comprising provisioninga set of computing resources in the networked computing environmentbased on the forecasted network traffic.
 3. The computer-implementedmethod of claim 1, the derivative vector plot comprising a K^(th)derivative vector plot being generated by transforming the set of datapoints using a mathematical algorithm.
 4. The computer-implementedmethod of claim 3, further comprising outputting a network trafficprojection based on the forecasting.
 5. The computer-implemented methodof claim 4, the network traffic projection being generated byintegrating K initial conditions a K quantity of times using apredetermined numerical technique.
 6. The computer-implemented method ofclaim 3, the mathematical algorithm comprising a fourth orderRunge-Kutta method.
 7. The computer-implemented method of claim 1, thenetworked computing environment comprising a cloud computingenvironment.
 8. A system for provisioning computing resources usingpredictive modeling in a networked computing environment, comprising: amemory medium comprising instructions; a bus coupled to the memorymedium; and a processor coupled to the bus that when executing theinstructions causes the system to: segment a set of graphical curves ofnetwork data traffic versus time generated from historical logs ofnetwork traffic into a set of predetermined time intervals to yield aset of time interval curves; overlay and fit the set of time intervalcurves to yield a set of best fit overlaying curves; generate aderivative vector plot based on a set of data points of the set of bestfit overlaying curves; and forecast network traffic in the networkedcomputing environment based on the derivative vector plot; and modify anallocation of a set of computing resources in the networked computingenvironment based on the forecasted network traffic.
 9. The system ofclaim 8, the memory medium further comprising instructions for causingthe system to provision a set of computing resources in the networkedcomputing environment based on the forecasted network traffic.
 10. Thesystem of claim 8, the derivative vector plot comprising a K^(th)derivative vector plot, the memory medium further comprisinginstructions for causing the system to transforming the set of datapoints using a mathematical algorithm to yield the K^(th) derivativevector plot.
 11. The system of claim 10, the memory medium furthercomprising instructions for causing the system to output a networktraffic projection based on the forecasting.
 12. The system of claim 11,the network traffic projection being generated by integrating K initialconditions of a K quantity of times using a predetermined numericaltechnique.
 13. The system of claim 10, the mathematical algorithmcomprising a fourth order Runge-Kutta method.
 14. The system of claim 8,the networked computing environment comprising a cloud computingenvironment.
 15. A computer program product for provisioning computingresources using predictive modeling in a networked computingenvironment, the computer program product comprising a computer readablestorage device, and program instructions stored on the computer readablestorage device, to: segment a set of graphical curves of network datatraffic versus time generated from historical logs of network trafficinto a set of predetermined time intervals to yield a set of timeinterval curves; overlay and fit the set of time interval curves toyield a set of best fit overlaying curves; generate a derivative vectorplot based on a set of data points of the set of best fit overlayingcurves; and forecast network traffic in the networked computingenvironment based on the derivative vector plot; and modify anallocation of a set of computing resources in the networked computingenvironment based on the forecasted network traffic.
 16. The computerprogram product of claim 15, the computer readable storage devicefurther comprising instructions to provision a set of computingresources in the networked computing environment based on the forecastednetwork traffic.
 17. The computer program product of claim 15, thederivative vector plot comprising a K^(th) derivative vector plot, thecomputer readable storage device further comprising instructions totransforming the set of data points using a mathematical algorithm toyield the K^(th) derivative vector plot.
 18. The computer programproduct of claim 17, the computer readable storage device furthercomprising instructions to output a network traffic projection based onthe forecasting.
 19. The computer program product of claim 18, thenetwork traffic projection being generated by integrating K initialconditions a K quantity of times using a predetermined numericaltechnique.
 20. The computer program product of claim 17, themathematical algorithm comprising a fourth order Runge-Kutta method. 21.The computer program product of claim 15, the networked computingenvironment comprising a cloud computing environment.
 22. A method fordeploying a system for provisioning computing resources using predictivemodeling in a networked computing environment, comprising: providing acomputer infrastructure being operable to: segment a set of graphicalcurves of network data traffic versus time generated from historicallogs of network traffic into a set of predetermined time intervals toyield a set of time interval curves; overlay and fit the set of timeinterval curves to yield a set of best fit overlaying curves; generate aderivative vector plot based on a set of data points of the set of bestfit overlaying curves; and forecast network traffic in the networkedcomputing environment based on the derivative vector plot; and modify anallocation of a set of computing resources in the networked computingenvironment based on the forecasted network traffic.